Machinery's Handbook, 31st Edition
Spring Design
333
Hook
Hinged
Straight Offset Straight Torsion Fig. 19. The Most Commonly Used Types of Ends for Torsion Springs 1.3
1.2
Round Wire
Square Wire and Rectangular Wire K × S = Total Stress
1.1
1.0
Spring Index 3 4 5 6 7 8 9 10111213141516
Fig. 20. Torsion Spring Stress Correction for Curvature Torque: Torque is a force applied to a moment arm and tends to produce rotation. Tor sion springs exert torque in a circular arc and the arms are rotated about the central axis. It should be noted that the stress produced is in bending, not in torsion. In the spring industry it is customary to specify torque in conjunction with the deflection or with the arms of a spring at a definite position. Formulas for torque are expressed in pound-inches. If ounce- inches are specified, it is necessary to divide this value by 16 in order to use the formulas. When a load is specified at a distance from a centerline, the torque is, of course, equal to the load multiplied by the distance. The load can be in pounds or ounces with the distances in inches or the load can be in grams or kilograms with the distance in centimeters or millimeters, but to use the design formulas, all values must be converted to pounds and inches. Design formulas for torque are based on the tangent to the arc of rotation and pre- sume that a rod is used to support the spring. The stress in bending caused by the moment P 3 R is identical in magnitude to the torque T , provided a rod is used. Theoretically, it makes no difference how or where the load is applied to the arms of torsion springs. Thus, in Fig. 21, the loads shown multiplied by their respective distances produce the same torque; i.e., 20 3 0.5 = 10 pound-inches; 10 3 1 = 10 pound-inches; and 5 3 2 = 10 pound-inches. To further simplify the understanding of torsion spring torque, observe in both Fig. 22 and Fig. 23 that although the turning force is in a circular arc the torque is not equal to P times the radius. The torque in both designs equals P 3 R because the spring rests against the support rod at point a .
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